The process of building ICs includes physical implementation of an IC design followed by verification of the IC design. During the verification process, a verification tool performs a large number of analyses to determine whether the physical IC design meets certain constraints. One such verification analysis is an electromigration analysis. Electromigration is the displacement of material caused by the gradual movement of ions in the material due to a momentum transfer between the electrons flowing through the material and the atoms that make up the material. Over time, electromigration may result in electrical short circuits and/or electrical open circuits in the material. The electromigration verification analysis is performed to determine whether conductor lines in the IC design will meet electromigration performance criteria.
As electrical AC current flows through AC conductor lines in an IC, the AC conductor lines heat up, which is an effect commonly referred to as Joule heating. The physical and geometric properties of the dielectrics and of the electrical conductors used in the manufacturing process limit the amount of heat that can be dissipated by those elements. Joule heating that is not adequately dissipated results in temperature rises in the IC that can detrimentally impact the electromigration performance of the conducting structures under evaluation and any adjacent conducting DC structures. In essence, Joule heating exacerbates electromigration.
The goal of the electromigration verification analysis is to determine whether Joule heating will degrade electromigration performance to an impermissible level. Unless a detailed thermal analysis fully representative of the three-dimensional aspects of the complete IC design is performed, it is very difficult to accurately estimate the temperature increase that will result and the extent to which it will affect electromigration performance. As a result, a simplified thermal analysis is sometimes employed during the verification process. The simplest such thermal analysis models each conductor line as a single line of unlimited length. In this type of analysis, a maximum line temperature rise is chosen as acceptable for the conductor line and the associated AC current needed to cause that rise is allowed for each conductor line in the design.
This simple thermal analysis has limitations. In particular, because of the low accuracy of the solution, it requires that the electromigration data be interpreted very conservatively. The analysis assumes that each conductor line reaches its maximum temperature and that all other conductor lines have also reached their maximum temperatures. Interpreting the electromigration data this conservatively can result in over-design penalties, in terms of both design cost and performance.
A known alternative to the simple thermal analysis is to analyze the full three-dimensional IC design for Joule heating of electrical routes to solve for the thermal profile in aggregate. Typically, such thermal solution formulations are simplified into lumped resistor network formulations. However, it is intractable to inject such formulations into the design cycle except in cases of designs that are very modest in size. For large designs that have hundreds of millions of conductor lines, it is generally intractable to run a full three-dimensional design thermal simulation, and even if it is possible to do so, it will likely result in wasted engineer hours and resources and lead to unacceptable project delays.
Accordingly, a need exists for a verification method that is capable of quickly and efficiently determining the temperature rise of DC conductor lines caused by Joule heating in nearby AC conductor lines in a way that avoids cost and performance penalties and unacceptable project delays.